I attempted to run a quasi test in ttool with a normal load and very low pressure (2kPa), I believe this particular tyre is a bias ply (it's from the database). I probably should have done a target load rather than setting the ground height manually, I thought 4.5cm compression was going to be close to my target of 2500N load but only ended up on 1835N.
What's clear is that first, it's not running on the rim, but also the majority of tyre wear is going to be near the shoulder. Not hard to see where the extra heat is coming from either from the side-on view.
(triple screen resolution; best to 'view image' or equivalent to get the full resolution)
Realistically I think it's reasonable to assume in real life this tyre would fail fairly quickly, through temperature and wear at that peak stress point out at the shoulders (note the cross-sectional view on the right hand side). We know rF2 doesn't do that sort of wear or structural fatigue though.
It's a shame we can't see more than a single tyre wear figure, because it hides the likely side effects of running a tyre like this in terms of uneven wear (and degradation at the focused contact areas). I haven't done any grip testing in ttool or the game with this sort of ultra low pressure, it's kind of hard to believe even with rF2's shortcomings in the tyre model that this doesn't produce considerably less grip than a normally-pressured tyre, and that difference would spiral out of control as rubber degradation kicks in.
Extra rolling resistance would indeed seem logical, but I think you'd also want some puncture mode of failure for tyres, and some sort of reasonable puncture/delamination effect too (in terms of graphics and handling)
For me this particular pressure shouldn't be selectable in the game (and I doubt it is, unless there's a crazy mod out there) so you don't even really need to allow for this sort of scenario with an intact tyre. You shouldn't reach this sort of state unless the tyre has already failed, and then all bets are off because the air that is being held in there in my test is probably the main thing keeping the rim off the track.
So, having actually done a few little tests, I'm now arriving back at the core question: does the game actually need to model this correctly? The only reason I can see you'd need to handle under about 100kPa in any normal tyre is in a slow leak puncture situation, and I suspect in that case you could handle it with separate specialised parameters (with some sort of accumulation leading to a complete failure, for example).
(I should also point out, this particular tyre and it looks like close to half the database tyres as well, don't have GaugePressure=0 in their suite of quasi tests. I believe extrapolation is limited after some spectacular failures early on in rF2, so if a tyre doesn't actually have tests run at that low pressure to build the lookup tables the effect will probably be a little off. But as above, I don't know how relevant this all is anyway)